Impact of Gravity in Thin-Layer Cell Electrodeposition

E. MOCSKOS; G. MARSHALL

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS

Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University

Lugar: Ohio, USA; Año: 2009 vol. 34 p. 90 - 101

1068-9613

Electrodeposition (ECD) in thin cells with different orientations relative to gravity leads to complex stable and unstable physicochemical hydrodynamic flows.Here we study the impact of gravity in these flows through a theoretical macroscopic 3D model and its numerical simulation.The model describes the diffusive, migratory and convective motion of ions in a fluid subject to an electric field through the Nernst-Planck, Poisson and Navier-Stokes equations, respectively.The equations are written in terms of dimensionless quantities, in particular, the gravity Grashof number, revealing the importance of gravitoconvection.The nonlinear system of partial differential equations is solved in a uniform grid using finite differences and a strongly implicit iterative scheme.In ECD in a cell in a horizontal position, our model predicts the evolution of two gravity driven convective rolls and concentration shells attached to each electrode: their birth, growth, expanding towards one another, collision and merging into a single roll invading the whole cell.In ECD in a  cell in vertical position, cathode above anode,  our model predicts that gravity induced rolls  and concentration shells remain locally attached to downwards growing fingers, thus global invasion of the cell by gravity induced rolls is suppressed leading to a stable stratified flow.In ECD in a cell in a vertical position, cathode below  anode, our model predicts the detachment of rolls and concentration shells from each electrode in the form of plumes, expanding towards one another, mixing, invading the whole cell and leading to an unstable stratified flow.For ECD whether in horizontal or vertical position, in the presence of growth, our model predicts the existence of an electrically driven vortex ring at the dendrite tip interacting with concentration shells and rolls, leading to complex helicoidal flows.Such structures are experimentally observed suggesting that ion transport underlying dendrite growth is remarkably well captured by our model.